The cost of designing and producing circuits is expensive. Accordingly, engineers need to ensure that their circuits operate according to their intended design. A number of computer applications have been developed which allow design engineers to simulate their circuits prior to actually incurring the cost of production. Some of these computer-aided engineering applications are based on “SPICE,” which was first developed by the University of California at Berkeley and later refined by a number of institutions, including the Georgia Institute of Technology. The SPICE-based applications provide design engineers with the necessary tools to create, test, and simulate circuits on a computer.
A limitation of the SPICE-based application is that it provides a limited number of standard circuit analysis. Such standard analysis includes alternating current (ac) analysis, transient analysis, operating point analysis, direct current (DC) sweep analysis and others. Typically, these analysis are performed using nominal values for the parameters of the circuit design. Accordingly, for a designer to see the effects of parameter tolerance variation, typically the designer changes the parameter value and then runs a simulation. For complicated circuits, manually changing the parameter values is cumbersome and time-consuming, and is typically not practical. Furthermore, designers may also want statistical analysis of the desired circuit measurements based on parameter variations, such as, for example, sensitivity analysis, root summed square analysis, extreme value analysis and worst case analysis, to name of few. Such additional analysis are not available in SPICE-based applications. Other customizable analysis may also be desired which is also not available in SPICE-based applications.
In the prior art, some SPICE-based applications provide a parameter tolerance variations analysis called adjoint matrices. In the adjoint matrices technique, a simulation is performed and a matrices is created which can characterize variations in the output vector measurements by mathematical equations. The mathematical equations model the output vector measurements based on parameter tolerance variations. However, this technique is typically not accurate and not stable. Mainly because the modeling equations do not take into account non-linear response of the circuit components due to parameter tolerance variations. Thus, in addition for a need of additional analysis for SPICE-based applications, there is a need for analysis which provide more accurate and stable simulations when performing a parameter tolerance variation analysis.
Such needs are provided for by the invention described herein.